As cybersecurity challenges become increasingly severe and many new attacks emerge, Regular Expression Denial of Service (ReDoS) attack is one of most practical threats, which has not garnered widespread attentions yet in the industries. This attack exploits potential design flaws of regular expressions in web services, significantly degrading the performance of target systems and posing serious threats to service availability. Current detection methods typically require numerous known ReDoS vulnerability patterns which are generated by ever attacked service servers. Therefore, a platform for sharing ReDoS cyber threat intelligence (CTI) is crucial, however, the traditional CTI sharing platforms bear the issues of data privacy leakage and lack of sufficient incentives for sharing their CTI. In this paper, we propose a blockchain based ReDoS CTI sharing mechanism to preserve CTI privacy and provide evolutionary game theory compatible incentives for CTI contributors. In our design, considering he distributed nature of ReDoS CTI contributors, we construct a ReDoS CTI sharing platform based on the consortium blockchain infrastructure, where all the CTI sharing related records are stored in a secure and immutable manner. To prevent potential CTI privacy leakage risks due to the transparency property of block data, we design an attribute-based encryption based CTI access control protocol, enabling ciphertext search functionality while preserving CTI data privacy. We further design an incentive mechanism based on evolutionary game theory to encourage stakeholders to actively share high-quality ReDoS CTI, where the value of ReDoS CTI is determined by the effectiveness in successfully defense against ReDos attacks. Simulation and real data based experimental results demonstrate the efficiency of our proposed system. Our study provides a blockchain based CTI sharing solution to encourage valuable ReDoS CTI shared effectively and efficiently in a privacy preserved way.